a. csaszar introduced and extensively studied the notion of generalized opensets. following csazar, we introduce a new notion hyperconnected. we study some specicproperties about connected and hyperconnected in generalized topological spaces. finally, wecharacterize the connected component in generalized topological spaces.

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear s...

We introduce and use the concept of (∈γ ,∈γ ∨qδ)-fuzzy (left, right, bi-) ideals to study the structural properties of a non-associative algebraic ordered structure. We characterize an intra-regular ordered AGgroupoid by these generalized fuzzy ideals. 2010 AMS Classification: 06F05, 20M12, 08A72

Generalized scalar operators were introduced by C. Foia~ [4] and a detailed study of such operators can be found in the monograph [3]. An important subclass consists of regular generalized scalar operators which enjoy properties not shared by all generalized scalar operators. For example, the sum and product of commuting generalized scalar operators S and T need not be generalized scalar operat...

in this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. afterwards, the a...

Fuzzy valued measure is a mapping which maps a σalgebra to a set of fuzzy set with convex compact σlevel defined on banach space (β). In this paper, we investigate the notion of decomposition and representation of fuzzy valued measure (F.V.M) is given in the sequence of singular valued measure. Also we have been studied and develop the notion of integrals with the aid of F.V.M under closed inte...